Consider the functions \( f(x)=7 x+8 \) and \( g(x)=\frac{1}{7}(x-8) \). (a) Find \( f(g(x)) \). (b) Find \( g(f(x) \) ). (c) Determine whether the functions \( f \) and \( g \) are inverses of each other. (a) What is \( f(g(x)) \) ? \( f(g(x))=x \) (Simplify your answer.) Give any values of \( x \) that need to be excluded from \( f(g(x)) \). Select the correct choice below and fill in any answer boxes within your choice. A. \( x \neq \square \). No valuds should be excluded from the domain. (Use a comma to separate answers as needed.) B. No

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another meth Write all numbers as integers or simplified fractions. \[ \begin{array}{l}7 x+7 y=-19 \\ \\ -9 x-5 y=4 \\ \text { Part: } 0 / 2 \\ \text { Part } 1 \text { of } 2 \\ \text { Evaluate the determinants } D_{1} D_{x} \text {, and } D_{y} \\ D=\square\end{array} \] \( \square \)

Question 2 of 25 After the drama club sold 100 tickets to a show, it had \( \$ 300 \) in profit. After the next show, it had sold a total of 200 tickets and had a total of \( \$ 700 \) profit. Which equation models the total profit, \( y \), based on the number of tickets sold, \( x \) ?

Use the elimination method to find all solutions of the system: \( \left\{\begin{array}{l}x^{2}-2 y=7 \\ x^{2}+5 y=14\end{array}\right. \) The two solutions of the system are: (the one with \( x<0 \) is) \( x=\square \) \( y=\square \) (the one with \( x>0 \) is) \( x=\square \) \( y=\square \)

Find the solutions. \( \left\{\begin{array}{l}x^{2}-4 y=29 \\ x^{2}+2 y=23\end{array}\right. \) > Next Question

4. \( x^{2}-6 x+8 \leq 0 \)